D-modules and harmonic analysis on semisimple Lie groups

Tuesday, 31-October-2023 

Abstract

Harish-Chandra developed harmonic analysis on semisimple Lie groups to prove his analogue of Plancherel theorem. His tehniques were analytic in nature. Beilinson and Bernstein developed the localization theory of representations of such groups to prove the Kazhdan-Lusztig conjectures using D-module theory. We are going to discuss, in non-technical terms, how the methods of the latter can simplify and amplify some arguments in the former.